This is the website/blog of Philosopher Stephen Law. Stephen is Provost of Centre for Inquiry UK, Reader in philosophy at Heythrop College, University of London, and editor of the Royal Institute of Philosophy journal THINK. He has published several books (see sidebar). His other blog is THE OUTER LIMITS: http://www.centerforinquiry.net/blogs/blibnblob
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Monday, August 11, 2014

The Mirror Puzzle

4. The Mirror Puzzle

(This is a chapter I wrote for a children's philosophy book called The Outer Limits (now part of The Complete Philosophy Files). This chapter was thought too abstract by the editors, and was not included).

Sometimes it is the things that are most
familiar to us that turn out to be the most deeply puzzling. Take mirrors, for
example. How many times do you see yourself reflected in a mirror each day?

1.ILLUSTRATE:
BOY LOOKING INTO A MIRROR

At least ten or twenty times, I
should think. Most of us never stop to think about what we see. But, as you are
about to discover, mirrors are very strange and puzzling things.

An adventure in the mirror

Aisha and Kobir are visiting
Kobir’s auntie. Auntie Anaximander lives in an enormous, fusty old house deep
in the moors.

2. THE BIG SPOOKY HOUSE IN THE
MOORS. LIGHTENING.

It’s a wild and stormy night and
the phone and power lines are down. Auntie Anaximander has gone off in her car
to report the powercut leaving Kobir and Aisha all alone in the dark house.

3: ILLUSTRATE: NERVOUS KOBIR AND
AISHA AT DOOR OF CREEPY COUNTRY HOUSE. STORY WEATHER. THEY ARE WAVING OFF
AUNTIE A WHO IS DRIVING A MORRIS MINOR. NB KOBIR IS OLD PHILOSOPHY FILES
CHARACTER WITH GOATIE BEARD HAS A RING ON HIS RIGHT HAND AND WATCH ON HIS LEFT
AND A HIS-LEFT-SIDE HAIR PARTING.

They light a candle and decide to
explore. After a while, Aisha and Kobir come across a huge echoing hall.

As they have nothing better to do,
they decide to sit down on the carpet in front of the mirror and play cards.
Outside, the wind howls and rumbles over the chimney tops. But inside it is
deathly quiet. The candle casts flickering shadows up the walls. Aisha opens
her notebook to keep score and starts to shuffle the cards. While she is shuffling,
Kobir stares distractedly into the vast mirror. And the more he stares, the
more perplexed he starts to look.

KOBIR: That’s really, really weird.

AISHA: What is?

KOBIR: Take a look at our reflection.

Kobir and Aisha both stare into the
mirror.

KOBIR: Notice anything odd?

AISHA: Odd?

KOBIR: You can see a mirror
version of yourself can’t you? And a mirror version of me.

AISHA: Of course.

KOBIR: But there’s something very,
very peculiar about our mirror selves. They are reversed.

AISHA: Reversed?

Kobir
stands up in front of the mirror.

KOBIR: Yes. Suppose this wasn’t a mirror but a big sheet of glass. And
suppose I was actually over there, where the mirror-version of myself appears
to be standing. Then my right hand, the one with the ring on, would be where my
left hand actually appears in the mirror. And my left hand, the one with the
watch on, would be where my right hand appears.

6.
ILLUSTRATE: KOBIR STANDING NEXT TO SEATED AISHA BEFORE MIRROR. WATCH ON LEFT
HAND AND RING ON RIGHT. HAIR PARTED TO HIS LEFT. HE IS LOOKING IN THE BIG, FULL
LENGTH MIRROR.

Kobir walks
closer to the mirror, so that he’s staring right into the face of his
mirror-self.

Kobir: And look, my left eyebrow – the one I’m raising – appears where
my right eyebrow would be.

7. ILLUSTRATE:
KOBIR’S FACE AND ITS REFLECTION, WITH EYEBROW RAISED AS DESCRIBED. HAIR PARTED
TO HIS LEFT.

Isn’t that odd?

Kobir
is right about the reversal. When we look at Kobir in the mirror we see this:

8.
ILLUSTRATE: KOBIR STANDING LOOKING AT US, RING ON LEFT HAND AND WATCH ON RIGHT.
HAIR PARTED TO HIS RIGHT.

But
if Kobir was actually standing where his image appears to be standing, we would
see this:

9.
IDENTICAL IMAGE BUT WATCH ON LEFT HAND AND RING ON RIGHT. HAIR PARTED TO HIS
LEFT.

See?
Kobir’s left and right sides have been reversed.

Why do mirrors reverse left
to right, but not top to bottom?

Aisha
just wants to play cards. She’s irritated by Kobir’s question.

AISHA: Why is it odd?

KOBIR: Well, mirrors reverse us left
to right. So why don’t they also reverse us top to bottom.

AISHA: Top to bottom?

KOBIR: Yes, in the mirror, what’s
top and bottom is the same. Take a look: my head is still at the top and my
feet are still at the bottom. But my left and right sides are swapped round.

AISHA: True.

KOBIR: So my question is: Why
do mirrors reverse one way, but not the other? It’s very, very strange.

Kobir is
correct. In a mirror image, what’s at the top and what’s at the bottom remains
unchanged. But left and right are switched. That is why the word “ambulance” is
painted in reverse on the front of an ambulance.

10.
ILLUSTRATE: AMBULANCE WITH WORD “AMBULANCE” REVERSED ACROSS THE FRONT.

The word is
seen by other motorists in their rear view mirrors. Because mirrors reverse
left to right, and because the word “ambulance” is itself reversed left to
right, a rear view mirror has the effect of turning the word the correct way
round so it can easily be read.

11.
ILLUSTRATE: SAME AMBULANCE SEEN IN REAR VIEW MIRROR: NOW THE WORD IS RIGHT WAY
ROUND (DRIVER ON OTHER SIDE, OF COURSE)

An ancient and infernal puzzle

Why do mirrors reverse left and right, but
not top and bottom? Some of the world’s greatest minds – including that of the
Ancient Greek philosopher Plato – have struggled with and been defeated by this
infernal mystery.

12.ANCIENT
GREEK IN BEARD AND ROBE LOOKING IN MIRROR AND THINKING BUBBLE: “WHY DO
MIRRORS REVERSE LEFT/RIGHT BUT NOT TOP/BOTTOM?”

Can Kobir
and Aisha do any better? Can you?

Perhaps. But before we try to come
up with an explanation that might
work, let’s take a look at a few explanations that definitely don’t work.

“Doesn’t it depend on which we up we
are?”

Aisha can
now see the puzzle.

AISHA: Hmm. I’m not sure why mirrors do what they do. Now you mention
it, I suppose that is rather
peculiar.

KOBIR: It’s weird!

Suddenly,
Aisha thinks she has the solution.

AISHA: Doesn’t it
all depend on which way up we are? If
we lay down, then it would be top and
bottom that are reversed, not left and right.

KOBIR: I don’t
think so. Let’s try.

Kobir moves the candle safely to
one side. Then they both lie on their sides and stare at themselves.

13.ILLUSTRATE; T AND A LOOKING INTO
MIRROR AS THEY LAY ON THEIR SIDES. KOBIR IS WIGGLING FINGERS OF RIGHT HAND (THE
ONE WITH RING).

KOBIR: You see? If
I was over there, my right hand – the one with the ring – would be where my
left hand appears. My left and right sides are still reversed.

AISHA: True. And
our tops and bottoms are still the right way round.

KOBIR: So the
mirror flips things around left to right but not top to bottom no matter what
way up we may happen to be in front
of it.

AISHA: Hmm. I
guess you’re right.

KOBIR: I am
right. The reversal has nothing to do with which way up we are. Actually it doesn’t have anything to do with which way up
the thing we are looking at is, or
which way up the mirror is, either.
Mirrors always reverse left to right
but not top to bottom.

You can confirm this for yourself.
Here’s the word “ambulance” reversed from left to right:

14.ILLUSTRATE:
“AMBULANCE” REVERSED L/R

Try putting this page up in front of a
mirror. Because the mirror also reverses left and right, the word gets switched
round the right way again, doesn’t it?

15.ILLUSTRATE:
MIRROR IN FRONT OF REVERSED WORD “AMBULANCE”, IN MIRROR THE WORD IS ROUND THE
RIGHT WAY.

Now let’s try turning you, the observer to see if that has any
effect on how the word is reversed. Hold the book upright, but turn your head
sideways like this.

16.ILLUSTRATE. KID BEFORE MIRROR:
HE IS HOLDING BOOK UPRIGHT WITH HEAD TILTED OVER SIDEWAYS.

See? It doesn’t matter which way up
you are. The mirror still flips the
letters back the right way. It still reverses them left to right to make them
readable again.

Now let’s
try rotating the book 90 degrees, like this.

17.ILLUSTRATE: SAME KID BEFORE
MIRROR, NOW WITH HEAD UPRIGHT BUT HOLDING THE BOOK SIDEWAYS ON.

Does that have any effect on how
the word appears? No. The word “ambulance” is still legible. So it doesn’t matter which way up the word is
either.

Maybe you’re thinking that the solution
has something to do with which way up the
mirror is. But it doesn’t. Turn the mirror upside down, and the image will
remain exactly the same.

So it
doesn’t matter which way up we are,
which we up the thing we are looking at
is, or even which way up the mirror
is, a mirror always reverses left to
right but not top to bottom.

18.ILLUSTRATE: KOBIR AND AISHA
LOOKING AT THEMSELVES IN MIRROR 9STILL IN THE SPOOKY ROOM): BIG THOUGH BUBBLE
WITH QUESTION MARK IN IT COMING OUT OF THEIR HEADS. THEY LOOK PERPLEXED.

The more you grapple with this
mystery, the deeper and more profound it seems to become. In fact, the more you
think about mirrors, the more they seem to take on a rather spooky, almost magical quality. Just why do mirrors do what they do?

I think I know the solution, or at least a
part of it.

Aisha
and Kobir heard a distant bang followed by echoing footsteps. After a minute or
so, Auntie Anaximander’s damp features appear round the doorway.

25.ILLUSTRATE:. ANAXIMANDER IN
RAINCOAT, LOOKING ROUND DOOR OF ROOM.

ANAXIMANDER: Ah.
There you are! Power should be back on soon. What have you been up to?

Auntie Anaximander takes off her
raincaot and shakes out the raindrops, spraying them across the room. A few
droplets land on the pages of Aisha’s open notebook.

26. ILLUSTRATE: RAINDROPS ACROSS
THIS PAGE.

Aisha and Kobir explain that they
had been discussing why mirrors reverse left and right, but not top and bottom.
Auntie Anaximander, who loves puzzles such as this, sits down on the carpet beside
them. She thinks hard for a moment or two.

ANAXIMANDER: You
know, in a sense, a mirror doesn’t reverse anything at all.

AISHA: In what
sense?

ANAXIMANDER: Well
suppose we hold a clock up in front of a mirror, like this.

Anaximander draws this picture on a page
of Aisha’s notebook.

27.ILLUSTRATE: CLOCK AND ITS
REFLECTION IN MIRROR

ANAXIMANDER: Now
let’s draw arrows linking each number on the clock face with the same number
reflected in the mirror.

Anaximander adds arrows
like this:

28.ILLUSTRATE: AS ABOVE BUT WITH
ARROW DRAWN FROM EACH NUMBER ON CLOCK FACE TO IT’S IMAGE IN THE MIRROR (I WILL
PROVIDE ROUGH)

ANAXIMANDER:
These arrows show that the way the mirror reflects is entirely symmetrical in every direction. The arrows don’t cross
over top to bottom. But neither do they
cross over left to right.

KOBIR: You know,
I think you’re right. In a sense, nothing
gets reversed!

Auntie Anaximanderis right. The way in which the mirror
reflects what’s in front of it is perfectly symmetrical. It is not as if a
mirror reflects rays of light differently depending on whether they are coming
from your left and right sides rather than your top and bottom. The light is
reflected in the same way no matter where it happens to land on the mirror.

So the puzzle has absolutely nothing to
do with how light behaves.

KOBIR: But hang
on. We said, didn’t we, that the left and right are swapped round? And that top
and bottom are unchanged?

ANAXIMANDER: Yes.
That is how we would normally
describe what we see.

AISHA: Normally?

ANAXIMANDER: If
we were to replace this mirror with a sheet of glass, and you were to walk
round the glass and stand on the other side, looking towards me, in the exact
spot you currently see your mirror-self standing, then what would I, standing
over here, see?

KOBIR: You would
see my right hand to your left, and my left hand to your right.

29.ILLUSTRATE: WE ARE LOOKING AT
KOBIR BEHIND BIG SHEET OF GLASS. AUNTIE ANAXIMANDER AND AISHA ARE THIS SIDE,
WATCHING.

ANAXIMANDER:
True. And of course, when we look at your mirror-image, your left hand appears
where your right hand would be if you were standing there, and your right hand
appears where your left would be. That’s
why we said that the mirror-version of you is reversed left to right. Correct?

KOBIR: Yes.

ANAXIMANDER: But
notice that we have just taken something
for granted: the axis about which we rotate you when we imagine you over
there.

AISHA: The what?

ANAXIMANDER: When
we turn something round, we rotate it about an axis, don’t we? A spinning top,
for example, rotates around a vertical
axis, doesn’t it?

KOBIR: That’s right. That’s how I would get over there, by walking round the
mirror like that.

ANAXIMANDER: Of
course. But what if we were to get you over there not by rotating you around a vertical axis, but a round a horizontal axis? What would happen then?

KOBIR: I’m not
sure. Let’s draw it to see.

Kobir now draws this picture:

33.ILLUSTRATE: AS ABOVE, BUT KOBIR
IS NOW ROTATED AROUND HOROIZONTAL AXIS, LEAVING HIM STANDING ON HIS HEAD BEHIND
THE MIRROR (I WILL PROVIDE ROUGHS)

ANAXIMANDER: Now
see what happens! You are standing on your head. And, compared to your mirror
image, your left and right sides aren’t
switched round.

34.SPLIT ILLUSTRATION: CAPTION 1
“MIRROR IMAGE” RING ON KOBIR’S LEFT, WATCH ON HIS RIGHT, PARTING TO HIS RIGHT.
CAPTION 2: “KOBIR STANDING ON HIS HEAD” KOBIR UPSIDE, BUT NOT REVERSED LEFT TO
RIGHT.

Your right hand
stays over to the right, just as it appears in the mirror. But top and bottom have been switched round!

AISHA: Wow!
You’re right.

ANAXIMANDER: So
you see, the reason we say mirrors reverse left and right but not top and
bottom is due to the fact that we take for granted a particular axis of rotation. But we could just as
easily choose a horizontal axis. Then it would be true to say that a mirror
reverses top to bottom but not left to right.

I think Auntie Anaximander is
correct. She really has hit on the explanation of why mirrors reverse left to
right but not top-to bottom. Yes, it’s true to say mirrors reverse left to
right, but only if we choose a vertical axis of rotation. Choose a horizontal
axis and they then reverse top to bottom.

Kobir furrows his brow.

KOBIR: But why do we take the vertical axis for
granted?

ANAXIMANDER:
Because people aren’t in the habit of flying through the air like pigeons and
settling on their heads. When people normally
rotate, it’s almost always about a vertical axis. So we just took for granted a vertical axis of
rotation in this case too.

Suddenly the electricity comes on. The
chandeliers above their heads flood the hall with light. Auntie Anaximander
jumps up and blows out the candle. She suggests they all go downstairs for some
hot chocolate. So they do.

35: ILLUSTRATE: AUNTIE, KOBIR AND AISHA
LEAVING THE NOW VERY BRIGHTLY-LIT HALL.

The door puzzle

I believe Auntie Anaximander is right:
this puzzle about why mirrors do what they do is created by our not noticing
what we have taken for granted. To
solve the puzzle, we need to take a step back and start questioning what we
taken for granted.

Actually, I have noticed a similar puzzle
about doors. Walk though a door that opens on your left and turn round to come
back through it, and the door now opens on your right. But pass through a door
that opens at the top (like a cat-flap) and turn to come back through it and
the door still opens at the top.

36.ILLUSTRATE: DOOR OPENS AT TOP
LIKE A CAT FLAP.

Why does passing through a door
reverse the way it opens from left to right, but not from top to bottom? What
explains the difference?

The
solution is much the same as Auntie Anaximander’s solution to the mirror
puzzle. When you pass through a left-opening door and turn around to come back
through it, you would normally rotate
about a vertical axis, like this:

37.ILLUSTRATE: AS FOR PREVIOUS
ILLUSTRATION BUT ONE: EXCEPT WITH AXIS OF ROTATION ADDED: SEE ROUGH.

Then the door
that opened on the left would still open the left on the way back though it,
but a door that opened at the bottom would now open at the top. We say that
left and right are reversed but not top and bottom only because we take for
granted a particular axis of rotation.

In space,
where we are weightless, the axis of rotation about which we choose to rotate
when turning to come back through a door is less likely to be the vertical
axis. You could just as easily spin about a horizontal axis instead.

So, after
years in space, it might start to seem as natural to you to say that a door
that opens at the top opens at the bottom when you come back through it as it
does to say that a door that opens on the left opens on the right when you
return though it.

For
creatures that live in a weightless environment, where it’s as easy to rotate
about one axis as it is to rotate about the other, perhaps neither the mirror
puzzle nor the door puzzle would even be
puzzles!

The “ambulance” test

Perhaps you are still not convinced
by Auntie Anaximander’s solution. If so, here’s another little experiment you
can perform. We said that in a mirror the word “ambulance” is reversed left to
right and not top to bottom. So now write out, on a separate piece of paper
next to the word “ambulance”, the left-right reversed version of the word. It
should look like this:

40. ILLUSTRATE: SEE ROUGH.

You have kept what’s at the top at
the top and what’s at the bottom at the bottom, but the right hand end of the
word has become its left hand end.

But now
suppose that mirrors reversed, not left to right, but top to bottom. What would
that look like? What would we see then?

Try to draw
it. This time, write on a separate piece of paper underneath the word
“ambulance” how the word would look if what’s at the top becomes what’s at the
bottom, but the left and right ends remain unchanged. It should look like this:

41.ILLUSTRATE: SEE ROUGH

The word is flipped top to bottom
but not left right.

But now
look very closely at the two reversed
words.

42.ILLUSTRATE: THE TWO REVERSED
WORDS (SEE ROUGH), LABELLED “REVERSED TOP TO BOTTOM” AND “REVERSED LEFT TO
RIGHT”.

Notice anything peculiar?

The two reversed
versions of the word that you have written are actually exactly the same! Turn the second one round to check, like this:

43.ILLUSTRATE: SEE ROUGH (LABEL
LEFT RIGHT REVERSED AND TOP BOTTOM REVERSED)

The left-right reversed version of
the word just is the top-bottom
reversed version.

So why did
we call one left-right reversed and the other the top-bottom reversed? Because
we just assumed a different axis of rotation in each case. Whether we describe
an image as left/right reversed or top/bottom reversed all depends on what axis
of rotation we choose.

When science can’t help us

So I think we have solved the
puzzle (or at least we solved this version
of it).

Here’s an
interesting fact about the mirror puzzle: it can’t be solved by doing science. It can only be solved by thinking
philosophically. We didn’t have to any scientific research into how light and
mirrors behave. We didn’t have to investigate how our brains work.

Even if we
had done that sort of scientific research, it wouldn’t have solved the puzzle.
In order to solve the puzzle, we need to stop
doing science and start doing philosophy. It’s a puzzle that can be solved just by thinking.

45. ILLUSTRATE: ME SLUMPED IN
CHAIR, LABELLED “PHILOSOPHER AT WORK”

People
sometimes assume that all our questions can be answered by science. They would
just assume that the mirror puzzle must have a scientific solution. But it
turns out that the mirror puzzle is a puzzle that science can’t solve.

6 comments:

I disagree. Math/science can solve it. A mirror only reverses (transforms) everything on the perpendicular axis of the mirror surface. If the mirror is positoned to the north of the subject, the subject front will be pointing south (reversed) but the subject's left hand will be pointing west in both cases (not reversed).

However, 'left' and 'right' itself is defined relative to front and back (AND top/bottom), which is reversed by the mirror. This means your mirror image will switch left and right as well, just because of the transformation of front and back.

If your mirror is placed above you, the top/bottom axis is reversed and your mirror image is standing upside down (front and back remaining the same this time). Because left-right is also relative to top/bottom, they are reversed for your mirror image.

It's terrible philosophy that passes off a simple science/math-problem as some philosophical mistery. All the mistery is only apparent, from ignorance and illusory perceptions.

"You know, in a sense, a mirror doesn’t reverse anything at all."

Not merely in some sense, but in actuality. It's in a 'sense' that it is reversed, in the human brain's perceptual sense. See Feynman: https://www.youtube.com/watch?v=6tuxLY94LXw: "It's a psychological problem." And it's gross equivication on the terms left and right, equating what is the refelection of a left arm for the actual right arm.

"Some of the world’s greatest minds – including that of the Ancient Greek philosopher Plato – have struggled with and been defeated by this infernal mystery."

Which ones were defeated by it?

Some ancient minds might be excused. Anyone following Pythagoras and other mathematicians shouldn't have been confused by this. A simple clarity of thought dismisses the problem immediately. Anyone with a spot of a scratch or any distinguishing mark on one hand and not the other realises that nothing is actually reversed. Anyone following Newton has no excude whatsoever.

Incidentally, a concave mirror will reverse images. If you stand at the right point your head will be down, and you left hand and its wrist watch will move to the right. https://www.youtube.com/watch?v=wvYduTBpbuA. Science class! Yeah!

This is science, and the scientific use of maths. It takes empirical science to explain this, not philosophy. Philosophy has no solution to this apparent problem. Philosophers can call on the science of course, but they shouldn't be passing off the science they are explaining as if it's philosophy; and much less should they be passing it off as philosophy and claiming it isn't science. That amounts to interdisciplinary plagiarism.

But that's philosophers for you. Trust philosophers to make not merely a mountain out of mole hill but a whole career, a whole discipline, out of an endless series of trivial mole hills.

Ron Murphy has a point about much of philosophy. However, there are genuine problems studied by philosophers (such as the problem of 'the external world', which is a question that concerns scientists as well as philosophers. The question can be stated briefly as "If our knowledge of the world is mediated through our senses and cognitive apparatus, then how do we know what the world is 'really' like, independently of how observers experience it?"). This is actually a tricky dilemma.

Approaches to it partly involve science, such as the study of human cognitive limitations that shape sense data in specific ways (for example, humans can only see limited wavelengths of light). There's also an element of psychology, such as the finding that humans are extremely good at selective attention (for a funny demonstration, watch this 5-minute clip http://youtu.be/UtKt8YF7dgQ).

This psychological finding then raises a speculative question: What if our experience of the world is a collective exercise in selective attention? What if we're all preoccupied with pretending there isn't a 500-pound gorilla in the room? What kind of strategies could we most easily and successfully employ to pull that off, and how would those strategies help to explain why we experience the world the way we do (of course, much depends on what we're trying to avoid noticing)? BTW, Herbert Fingarette discusses the relationship between self-deception and selective attention in his article "Self-Deception Needs No Explaining", as well as his book 'Self-Deception'. His writing is non-technical, so is an easy way to get into the topic.

Of course, there are many proposed solutions to the problem of 'the external world'. It is always helpful to pay careful attention to shifts in meaning between different contexts, for words like 'external' and related terms. It has been argued that failure to do so with regard to the concept of 'causation' plays a central role in the problem of the 'external world' and related issues, more about that here: http://commons.pacificu.edu/eip/vol15/iss2/5/

A major problem with philosophy is, if you're attempting to formulate a substantial thesis that is purely discursive or theoretical, you're almost certainly going to drift into semantic indeterminacy. More on this here:http://whyphilosophyfails.com/

Ways to avoid this include anchoring your arguments to empirical data (e.g. from psychology or physics), and/or relying on negative arguments that show other theses to be internally logically inconsistent or unsupported by the 'facts' they claim to be supported by.

In that last approach, a viable strategy is to propose alternative interpretations of those 'facts', that do not support the thesis but which are hitherto unfalsifiable (this was a strategy favoured by the later Wittgenstein, in the famously bizarre thought-experiments he used to undercut the theories of meaning that underpinned certain philosophical 'problems' like the Sorites Paradox). So, yes, much of philosophy is almost certainly semantically indeterminate (a less charitable critic would say 'non-sensical'). Once you're immersed in a purely discursive enquiry, you tend to quickly lose sight of the boundary between sense and nonsense.

It's a psychological problem, so more philosophy isn't the solution. The only solution I know is to stick closely to the methods and standards of empirical science and logic, and be mindful of alternative interpretations of 'data', while being open to theoretical possibilities. Arguably, that's not really a 'philosophical' approach. So the problems are 'philosophical', in the sense that they feature in the literature called 'philosophy', but viable solutions would probably involve a fair bit of science and logic.

I think the critics have a point, it is inadvisable to try and do 'pure philosophy' (or any purely discursive or theoretical enquiry) if you're looking to make sense. A more promising approach is what is now called 'experimental philosophy', which combines theoretical speculation with scientific data, mainly from psychology.

According to Geert Arys (above) and others, our idea of reflections in mirrors comes from the fact that they represent a reversal from back to front in some objectively true sense. But how is this supposedly privileged reversal realized?

Surely the answer is obtained by inverting and thereby contradicting Geert's own point: it happens because "back-front" is defined relative to left-right (AND top/bottom). This is the whole point of the term "relative" after all.

Broadly I agree with Stephen's discussion, although I also think that the contingencies associated with psychological aspects of the question tend to obscure a more interesting philosophical point. In particular, there is evidently no means of distinguishing mathematically between the world and its reflection except by imagining a direct comparison - a point which significantly concerned Immanuel Kant. eg. see http://philsci-archive.pitt.edu/713/1/parity.pdf.

As far as I can see, science plays little or no part in posing, let alone in solving this abstract question, and excepting the comparison of real-world examples, such as molecular enantiomers, the (abstract) concept that there is indeed a distinction between chiral counterparts seems to be foundational.

In this context, it is worth remarking that no two scientists will ever be able to establish whether or not they both perceive the same "handedness" in the world, (will they?). However, if there is no scientific fact of the matter, this indicates in turn that the apparent breaking of mirror-symmetry in certain sub-atomic processes must be illusory. (Who will still pretend that philosophical arguments have no part to play in scientific decision-making?)

Thank you, Philolinguist, also, especially for your suggestions and links regarding causality. I have found these extremely interesting (especially since the arguments there tend to corroborate my own views!)